The measure of the tapering of a large conic structure has always been made in the past substantially by approximations, i.e. not in a scientific manner. This, of course, constitutes a considerable limitation on the accuracy of the dimensions of manufactured tapering structures, and especially for structures pierced by a conic bore, the latter being conventionally the most difficult to measure and, thus, to manufacture. Expensive gages and gages ground to a specific shape, are now used to set the boring machine. Then a ball micrometer is used to measure the diameter at the larger end of the taper; but the level of precision of the measures is quite low. This is why supplemental strenuous work has to be done, usually by hand.
Mechanic blue is applied on the tapered end part of a large diameter shaft, and the end part is tried in the tapered bore of a wheel or the like for verifying contact therewith. If contact is not up to expectations, the bore surface must be scraped or manually finished, and the process is repeated until the required contacting relation is obtained. Such a process is labor intensive since it may take up to a couple of weeks to obtain a satisfactory result.
When measures of precision are to be taken in view of a final value, it is the intermediate measurement having the lowest level of precision that constitutes the bottle-neck of the accuracy of the final value. For example, if a final value A is to be determined by finding the value of variables B, C, and D, whereby A=B+C+D, with B being precise to 0.01 unit, C to 0.001 unit, and D to 0.0001 unit, then A will be precise only to up to the level of precision of the value B, i.e. to 0.01 unit.
A sine bar is a device for assisting in the measure of the slope of a structure having an inclined surface, through computations made accordingly with trigonometric laws. It is normally used by quality control inspectors in machine shops, tool rooms and the like, for finding and checking angles, measuring angles and tapers to determine center distances, etc . . . . The sine bar is usually made of two round discs fastened to a main intermediate steel bar. A sine bar comes normally at a single standard length, which is usually a five- or ten-inch length.
A set of various gage-blocks, of precisely-known dimensions, is provided with conventional sine bars, and a number thereof have to be alternately selected empirically to constitute two spaced "columns" of different height, thus making a virtual slope accordingly with the slope of the said structure-inclined surface. The sine bar is used cooperatively with these two columns of gage-blocks, with one disc supported by the smaller column and the other disc supported by the higher column. The gage-blocks are required in this process, because only limited sections of the sine bar disc can be utilized in setting up for angular work in connection with the usual angle plates and, therefore, the sine bar disc could not be used directly on the structure surface, the slope of which is to be measured.
It is also customary to supplement sine bar operation with said gage-blocks, with further direct reading on the barrel of a micrometer that adjusts the relative height with angular minutes of precision. A micrometer usually consists of two elements; a barrel and a thimble, the barrel operating in a screw having a large number of threads per inch, so that one turn moves the barrel and thimble a corresponding fraction of an inch.
When measuring the diameter of a given section of a cone member, a pair of inturned micrometers are usually provided at the two ends of a semi-circular or C-shaped compass-like member, wherein a given length or height is determined by the distance between the two micrometers. Inversely, when measuring the diameter of a given section of a conic bore in a bored structure, two out-turned micrometers are usually provided at the two outer ends of a straight rod-like member. The difficulty resides in the precise measure of the taper of such cone member or conic bore; as for now, the value thereof is obtained with poor accuracy and is at best approximate. Thus, the level of precision of the measure is low. Accordingly, cone members and members having conic bores cannot be manufactured beyond intermediate-to-low tolerance levels.